Gödei's Theorem seems to me to prove that Mechanism is false, that is, that minds cannot be explained as machines. So also has it seemed to many other people: almost every mathematical logician I have put the matter to has confessed to similar thoughts, but has felt reluctant to commit himself definitely until he could see the whole argument set out, with all objections fully stated and properly met. This I attempt to do.

page 120 note 1 Godel's original proof applies if the rule is such as to generate a primitive recursive class of additional formulae; v. § I init. and § 6 init. of his Lectures at the Institute of Advanced Study, Princeton, N.J., U.S.A., 1934. It is in fact sufficient that the class be recursively enumerable, v. Rosser, Barkley: “Extensions of some theorems of Godel and Church”, Journal of Symbolic Logic, Vol. 1, 1936, pp. 87–91.